Ponder This

June 2015

IBM's QRadar system keeps track of events by measuring something every second. It has an anomaly detection system that alerts the user when the current measurement is more than three standard deviations away from the average of all previous measurements.

An imaginary attacker is trying to deceive the system by slowly drifting the measurements, without violating the anomaly detection rule at any stage. If the first two authentic measurement were -100 and 100, then the second can be anywhere between -300 and 300 without triggering an alert.

The attacker can throw the measurements off quite fast. For example, the sequence {-100, 100, -300, 389, 786, 1318, -1284} is a legal sequence (every measurement is no more than three standard deviations from the average of the previous ones), spanning an interval length of 2602.

To make things more complex, we ask the question in two dimensions: where each measurement is a Gaussian integer (a complex number whose real and imaginary parts are both integers) and the attacker tries to maximize the area of the convex hull of the sequence.

Your task is to find a legal sequence of 9 measurements starting with -100i,100i that achieves a convex hull area of at least 7,700,000.

Please supply the solution in the following format: (-100,0),(100,0),(110,279), ...

Update (21/6):

Currently, the best solution is 7,720,004.

The standard deviation of n points is the square root of the average of the squared distance of these n points from their average. For example, the standard deviation of (-100,0),(100,0),(110,279) is 163.26.

Update (14/6):

We'll add a star to the best solver. Currently it is Alex Wagner with a convex hull of 7,719,775.

Make sure that every measurement is not exceeding 3 standard deviations from the mean of all the previous one.

We will post the names of those who submit a correct, original solution! If you don't want your name posted then please include such a statement in your submission!

We invite visitors to our website to submit an elegant solution. Send your submission to the ponder@il.ibm.com.

If you have any problems you think we might enjoy, please send them in. All replies should be sent to:ponder@il.ibm.com